This means that if we were to start at any point N and add up the positive terms
after that point in order, then the partial sums would be unbounded above. Likewise
if we added up the negative terms following N in order then the sequence of partial
sums would be unbounded below.
Question:
What happens if the very first term is already greater than a?
Question: How do we know that the sum ever reaches values greater than a?
Question: How do we know that the point k1 is ever reached?
It remains to put this all together and show that the partial sums sm converge
to a.
Question:
Try to prove this. (The simple
properties of the absolute value function may help.)